Work

Path Extendable Tournaments

Year: 2026

Type: article

Abstract: ABSTRACT A digraph is called path extendable if for every nonhamiltonian (directed) path in , there exists another path with the same initial and terminal vertices as , and for a vertex . Hence, path extendability implies paths of continuous lengths between every vertex pair. In earlier works of C. Thomassen and K. Zhang, it was shown that the condition of small or positive implies paths of continuous lengths between every vertex pair in a tournament , where is the irregularity of and denotes for the minimum number of paths of length 2 from to among all vertex pairs . Motivated by these results, we study sufficient conditions in terms of and that guarantee a tournament is path extendable. We prove that (1) a tournament is path extendable if , and (2) a tournament is path extendable if . As an application, we deduce that almost all random tournaments are path extendable.

Source: Journal of Graph Theory

DOI: 10.1002/jgt.70127

Authors: Zan‐Bo Zhang, Weihua He, Hajo Broersma, Xiaoyan Zhang

Institutions: Guangdong University Of Finances and Economics, Guangdong University of Finance, Guangdong University of Technology, University of Twente, Nanjing Normal University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Basic and Applied Basic Research Foundation of Guangdong Province

Awards: 芯片及网络设计中的图优化问题研究, G559540161